help-26

[wheat token]

.close

[topaz sinew]

Channel closed

Closed by @wheat token

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[glossy wadi]

Hello, I was wondering if anyone could assist me with this problem. I have followed the hint and found that we need to choose a M_n such that x - lnx >= ln(M_n) but I'm not sure where to go from here.

[topaz sinew]

@glossy wadi Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[inner dove]

Hints please

[icy sky]

what does the graph |z| = 25 look like?

[noble laurel]

@worthy storm Sir?

[worthy storm]

does your sir know you are asking this here?

[inner dove]

Circle

[inner dove]

What?

[icy sky]

so 75 times all the points does what?

[inner dove]

But that is z bar

Modulus sign no

[icy sky]

ive never seen that notation

[inner dove]

|zbar| not equals to zbar

It is just conjugate

[icy sky]

either way youre using zbar throughout the whole problem

it doesnt matter

[inner dove]

How to start solving?

[icy sky]

i gave you the first step

[noble laurel]

The answer is (a), circle.

[inner dove]

Bro i know that answer is circle

I am here to learn the process😭

[noble laurel]

The points with modulus 25

|z-bar|=25

means that they have distance 25 from the origin

So it is a circle, of radius 25

[inner dove]

But how

[noble laurel]

|z-bar|=25
means points on a circle of radius 25

[inner dove]

If it was -1+|z'|

But here they have no | | sign

[noble laurel]

yes ma'am let me continue my explanation

[inner dove]

Yes sir austin

[noble laurel]

amazing ma'am. so the points, they're on this circle. and then what we do is we scale all of them by 75, and then subtract 1 from the real part

they're right here

red circle

is zbar's

[icy sky]

what is your understanding of absolute value ciup?

[noble laurel]

once you scale them then they get to here

[inner dove]

I have said it is circle

[noble laurel]

its not absolute value

[worthy storm]

did your sir draw that

[noble laurel]

then when you subtract 1 from their real part, it shifts the circle to the left 1

[noble laurel]

yes

[icy sky]

ok, excuse what i said, the notation |.|

[inner dove]

I have said it will make circle

[icy sky]

how would you define it?

[inner dove]

Modulus

[noble laurel]

Ma'am, please ignore him I was explaining it just fine

[inner dove]

√x^2+y^2

Which makes circle

But in the qiestion do you feel same -1+75z'

Here it is not with modules sign

[noble laurel]

ma'am, I explained above what to do about the 75 and the -1

[inner dove]

It is not -1+75|z'|

[noble laurel]

yes

we know

the modulus being 25, tells you the points z-bar are somewhere on that circle

geometrically

so z-bar, not |z-bar|

are on the circle

do you understand that

[inner dove]

He is only stuck with this |z'|=r

It makes circle everyone knows

[noble laurel]

He?

[icy sky]

did i say that?

no

[inner dove]

You asked it third time

[noble laurel]

[icy sky]

i was asking you for your understanding of the notation

[inner dove]

And what I replied at first instance?

[icy sky]

that was good

[noble laurel]

I think he is ignoring you ma'am

[icy sky]

but the notation can be better seen as "distance from 0"

[worthy storm]

do you feel same -1+75z'

[inner dove]

How?

[icy sky]

ok im clearly being talked over

[noble laurel]

yes

[icy sky]

good fucking night

[inner dove]

You too

[noble laurel]

|z-bar|=25, means that z-bar, as a point in the complex plane, is on the circle of radius 25

[inner dove]

1:01

Pm India

[inner dove]

Of course i am done with it

I am comcern with -1+75

I know how to add and substract

[noble laurel]

great okay

[fair thorn]

this is the funniest thing ever

[inner dove]

But how can you sure about zbar

[noble laurel]

so z-bar*75 is on this circle then

[inner dove]

Zbar and |zbar| same?

[noble laurel]

ma'am...

[worthy storm]

that art makes me happier every time i see it

[noble laurel]

idk if this can be explained to you

[inner dove]

I meant x-iy doesn't equal to |x-iy|

[noble laurel]

you said of course you are done with it here

[fair thorn]

okay

@inner dove

[noble laurel]

and then you doubt here

[fair thorn]

the bars

mean the absolute value of the number

[inner dove]

I said about |zbar|=r makes circle

[fair thorn]

meaning the distance from the origin

[noble laurel]

yes

[fair thorn]

yes

good

[noble laurel]

it means the z-bar IS ON that CIRCLE

[fair thorn]

^

[noble laurel]

not |zbar| is on the circle

[inner dove]

Yes it is

[noble laurel]

it means z-bar

is on the circle

[fair thorn]

z-bar

not |z-bar|

[inner dove]

I am getting now

[worthy storm]

although, |z-bar| is in fact also on the circle

[fair thorn]

shhhh

bungo

[inner dove]

Yes it is on that circle

[fair thorn]

sthu

[noble laurel]

|z-bar| same as z-bar?

I am past this

[inner dove]

No no they are explain nicely

[fair thorn]

you evil man

[fair thorn]

yes i know, i am joking with him

[noble laurel]

@worthy storm you are explaining it nicely, please take over

[icy sky]

|zbar|=zbar for zbar=25+0i

[fair thorn]

@inner dove kya aap bharatiya ho?

[inner dove]

So you meant that zbar is on the circle

[worthy storm]

Here it is not with modules sign

[inner dove]

So any thing we add and substrcat

Will be circle

[fair thorn]

*modulus

...?

[inner dove]

Will be on the cicrle

[fair thorn]

what?

[noble laurel]

kya ise hindee mein karane se madad milegee?

[inner dove]

Haan ji

[fair thorn]

accha

[inner dove]

So they are just talking about the point

[fair thorn]

yes

the point lies on the circle

[inner dove]

First they gave us equation of circle

And claiming zbar on it

[noble laurel]

|z-bar|=25 ka arth hai ki bindu z-baar trijya 25 ke vrtt par hai

[fair thorn]

okay okay okay

@inner dove

let's say z = x+yi

okay?

that means z-bar = x-yi

okay?

[inner dove]

Yeah

[fair thorn]

now |x-yi| = sqrt(x^2 + y^2) = distance of number from origin

[inner dove]

x^2+y^2=625

[fair thorn]

no

[noble laurel]

so x is same as z-bar or is this with modules sign? He is past this

[fair thorn]

yes

[fair thorn]

wh?

she

[inner dove]

Let we feel it with xy

[fair thorn]

let me explain again, once

is that okay ciup?

[inner dove]

Yes yes

Okay

[fair thorn]

okay

[noble laurel]

[worthy storm]

Let we feel it with xy

[fair thorn]

so we know that

z-bar = x-yi

[inner dove]

Yes

[fair thorn]

|z-bar| = |x-yi| = 25

so this means

[inner dove]

x^2+y^2=625

[fair thorn]

that z-bar is 25 units away from the origin in some direction!

[fair thorn]

very good

austin sh

now

[inner dove]

Yes got it

And knew it

[fair thorn]

we know it's 25 units away

but we don't know what direction

it could be any direction

so this forms a circle w/ radius 25

of all the possible points where z-bar can be

now what we need to find is the shape formed by scaling this circle by 75 and adding -1

(to all the points on the circle, as in)

[noble laurel]

shall I bring back my diagram now sir Ren?

[fair thorn]

ji ha

[inner dove]

Lol

[worthy storm]

that diagram really says it all

[noble laurel]

it would never try to get sir banned 🙈

[inner dove]

A little doubt is we are scaling every zbar

[fair thorn]

yes

every possible z-bar is multiplied by 75

then we add -1

to every z-bar

[inner dove]

I got it now completely

[noble laurel]

add -1 I think you mean subtract 1

[inner dove]

Thank you so much all of you

[fair thorn]

no problem

[icy sky]

same thing

[fair thorn]

^^

dummkopf

[noble laurel]

No

[fair thorn]

austin shush okay

[icy sky]

oh my god, we are moving this elsewhere

[inner dove]

The main confusion was in mind about zbar and |zbar|

[fair thorn]

anything else, ciup?

[fair thorn]

alr

[noble laurel]

yahaan ekamaatr moorkh aap hee hain

[fair thorn]

|number| means distance of that number

[inner dove]

Good night sir?

[fair thorn]

from origin

[noble laurel]

aur garlic

[fair thorn]

good afternoon, ciup

[fair thorn]

austin not here.

[icy sky]

if you want to say something to me, say it to me

[fair thorn]

@inner dove anything else

[inner dove]

No i scare of some people

[fair thorn]

if not, do .close to close this channel

[inner dove]

Yes

[fair thorn]

??

what do you mean

[noble laurel]

our ma'am is a controversial figure ren

[inner dove]

I do not say directly

[fair thorn]

vo aapko nahi mujhe moorkh bula raha tha 🤣

[inner dove]

No no

Why will I say fool?

[noble laurel]

I am Ciup's master 😂

[fair thorn]

nahi nahi nahi

austin mujhe bol raha tha

[inner dove]

Austin is funny

I like the way he solve

.close

[topaz sinew]

Channel closed

Closed by @inner dove

Use .reopen if this was a mistake.

[inner dove]

@icy sky sorry

If any harsh word from me

Thanks all of you

[fair thorn]

no problem

[inner dove]

.close

[ivory sorrel]

this channel is closed

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[neon iron]

What is use of limits and what do we exactly get from limits?
Because in many cases... For example

f(x) = |x-4|/(x-4) for x ≠ 4 and 0 for x = 4
Here limits exist or not at x=4?
So Left hand limit is not equal to right hand limit is not equal to actual value at x=4
If everything is defined here
at x=4 and x≠4
Then why the hell we are finding limit here then

[worthy storm]

the limit does not exist

from the left it is -1 and from the right it is 1

[neon iron]

Yeah
But what is use of limits and what does limit even tell

[worthy storm]

it's useful for defining certain concepts precisely

such as continuity, derivatives, etc

most of calculus really

[neon iron]

But here in my question
If everything is defined in function
Then why are we even finding limit?

[worthy storm]

of this particular function?

probably just to give you practice to get used to the concept

[neon iron]

Yess

[worthy storm]

later you will do more useful things with it

[neon iron]

What limit actually tells you?

[neon iron]

Limit is suppose to tell you what value will it approach at certain value of x
But here already everything is given so what is even need to limit

<@&286206848099549185>

[topaz sinew]

@neon iron Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[quiet steppe]

is this a typo from my professor? It doesnt make sense to me, i would have expected the integral to be linear in every variable, which i think is what this wants to tell me? but arent the a_i on the wrong side? (for some reason we also specified a_i>0)

[pseudo jetty]

no this is correct

[topaz sinew]

@quiet steppe Has your question been resolved?

[quiet steppe]

wtf

ok i need to read into that that is counterintuitive

[pseudo jetty]

,w integral from -infty to infty of e^(-x^2)

[thorny flame]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by tearfox

[pseudo jetty]

,w integral from -infty to infty of e^(-(2x)^2)

[thorny flame]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by tearfox

[quiet steppe]

ok then it makes sense why for the proof he just wrote "substitution"

[topaz sinew]

Channel closed

Closed by @quiet steppe

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wheat token]

Why doesn't any of the solutions become multiplied by 2 or even divided by all of h?
Becoming 2(a-b2) /h=B1

[restive inlet]

not sure what you mean

[verbal crater]

have you tried the problem yourself?

[restive inlet]

can you show your work, are you getting something different

[wheat token]

Yeah I got 2(a-b2) then divided by /h, Ill try again

[restive inlet]

show your work

[verbal crater]

did you move b2 first and then multiplied by 2?

[wheat token]

From the original problem I did
2(a)=H(b1+b2)
2(a-b2)=H(b1)
2(a-b2) divided by h=b1

[restive inlet]

getting to

2(a-b2)=H(b1)
is invalid

you can't subtract out of the () like that

[wheat token]

Oh because of pemdas?

Oh I think I found what I did wrong, could this be it?
2(a)=H(b1+b2)
2(a)/h=b1+b2
(2a/h)-b2=b1

[restive inlet]

fix your capitlisation but yeh

[wheat token]

Sorry, thank you.

.close

[topaz sinew]

Channel closed

Closed by @wheat token

Use .reopen if this was a mistake.

[wheat token]

.reopen

[topaz sinew]

✅

[wheat token]

Sorry one more question, Lets say it was t^2/2pie^2=m/k and you're solving for m
Would the multiplication of k apply to the whole left side or just the numerator?

[restive inlet]

same thing

[wheat token]

Won't this be different since there were parenthesis in the last problem?

[restive inlet]

to multiply to a fraction, you'd multiply to the numerator

[wheat token]

Oh, I was never taught that, thank you.

.close

[topaz sinew]

Channel closed

Closed by @wheat token

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[calm shuttle]

Once I eliminate parts of a system with gaus, how do I actually examine the system? Like I am supposed to "discuss" a system, aka find different parameters for different solutions (determined, contradictory etc..) How do I cover all the bases to make sure I am actually finding all the possible answers; parameter combinations that give me different solutions to the system?
Thank you for taking your time to answer!

[topaz sinew]

@calm shuttle Has your question been resolved?

[topaz sinew]

@calm shuttle Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[wind pike]

I'm having a brain fart, can someone remind me how 2cosa cos240 in line 2 becomes 2(-1/2)cosa in line 3

Adding the two cosa cos240 = 2cosa cos240

Then it becomes 2(-1/2)cos a

[modern rock]

cos(240)=cos(180+60) which is quadrant 3 so cos is negative, hence it equals -cos(60) = -1/2

[wind pike]

I see... thanks!!

.solved

[topaz sinew]

Channel closed

Closed by @wind pike

Use .reopen if this was a mistake.

[wind pike]

This is so embarrasing

[modern rock]

lol

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[vague idol]

Hi, I was working with a hydrogen fuelling company and I had this task some time ago which we all in the company decided to abandon because our data gathering system was not ready. To simplify my question we will take water as an example:

given I have a series of tests where I fill water into a bucket and measure the time needed to fully fill the bucket. Lets assume the mass flow rate is constant. in any testseries.
given I repeat this test many times with different starting conditions each time. those different starting conditions would be different amounts of water in the bucket. so if the starting condition means that the bucket is half full, it will take less time to fill it completely in that specific case.
how can I create a function with all the values I gathered that can represent any curve of any given test with an input that declares the starting condition?
My idea when I drew all those functions in one plot and then fit a shape through it. However as Im lacking fundamental data analytics knowledge I wasnt sure this was the proper way to do it

[vague idol]

This is the actual data

How can one function represent all this data?

[potent flicker]

I think…

U overestimate the capacity of this server..

[vague idol]

Idk where I should aks

[potent flicker]

idk but

i guess

Tyler would help ?

nvm

[vague idol]

Who is tyler

[potent flicker]

oh i’m not sure

[half edge]

why is the curve 3d

is the only input factor the amount of water?

@vague idol

[vague idol]

There are so many input factors

Think of many testcases

And one curve was a test

Now find a function that describes all tests

That is what i am trying to do

One way would just be to lay a surface through the data

[topaz sinew]

@vague idol Has your question been resolved?

[topaz sinew]

@vague idol Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[slow plume]

Is it possible to further simplify this problem:

Budget: 100
List of items: [40,40,10,10]
Every item receives the same budget so budget divided by the length of the items array = 100 / 4 = 25

Then divide the 25 by the amount of each item 40/25 = 1.6 and so on

Resulting in 1.6, 1.6, 2.5, 2.5

Then converting them back into percentages by taking the sum of the results and dividing each result by that so: result / 8,2 * 100

Also what is this called? flipping percentages? But to summarize: my goal is to do this in the most efficient way.

I guess I could omit the part where I divide the 100 by the length of the array to begin with.

[topaz sinew]

@slow plume Has your question been resolved?

[slow plume]

<@&286206848099549185>

[topaz sinew]

@slow plume Has your question been resolved?

[slow plume]

.close

[topaz sinew]

Channel closed

Closed by @slow plume

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[plush oar]

how do you know when to adjust the limit when integrating

[plush oar]

do i always do it in every undefined and defined integral?

[lime perch]

wdym?

[plush oar]

the limits the x's

$\int _0^5:2.7e^{0.02x}$

for ex

[thorny flame]

Big Yannis

[plush oar]

so this is one i dont have to change the limits but on others one i do?

[lime perch]

i dont understand what you mean by changing the limits

why would you need to change them?

do you have an example of when theyre adjusted?

[plush oar]

adjusting them for example if you were doing u-substitution and u put 5 and 0 back into u

lemme find the one

this prob better example

[lime perch]

if youre doing substitution then you need to change the bounds

[plush oar]

this one i didnt tho?

didn't adjust the bounds

[lime perch]

because youre not using substitution

[plush oar]

i used u substitution to solve it tho'

[lime perch]

what is the original?

[lime perch]

,rotate

[lime perch]

okay so, you took u=0.02x

then your upper bound will become 0.02*5=0.1

and your lower bound will become 0.02*0=0

[plush oar]

oh right

im slow

lol

ok thanks

[lime perch]

does it make sense?

[plush oar]

yea

[lime perch]

$\int_a^b dx \rightarrow \int_{u(a)}^{u(b)} du$

[thorny flame]

Flappie

[plush oar]

got it

.close

[topaz sinew]

Channel closed

Closed by @plush oar

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[shut obsidian]

My teacher used a table for this, listing out all cases (putting these into "drawers" of = 0, = 1, = 2, = 3)

It was something like 12-15 cases, but for some reason I get much more

Obviously we can skip the cases where 7, 6, 5, 4 are in the first drawer

But then, starting at 3, we can get

3 3 1 0

3 0 1 3

3 1 3 0

Etc.

A lot of cases

Much more than 12-15, probably

[rapid vortex]

Are you familiar with the Pigeonhole Principle?

[shut obsidian]

Yes

[pale pagoda]

what is the Pythagoras Theorem

[shut obsidian]

(I don't have his solution available, he just showed it to me)

[rapid vortex]

#❓how-to-get-help

[pale pagoda]

what is this then

I just joined this server a minute ago

[cinder sequoia]

!occupied

[topaz sinew]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[rapid vortex]

occupied help channel

[pale pagoda]

please help

okay thanks

[rapid vortex]

!occupied

[topaz sinew]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[shut obsidian]

I really want to use his way though

With the cases

10-12 fast cases in a table aren't bad

[cinder sequoia]

well each of the 7 numbers has some residue mod 4, if at least four of the seven numbers have the same residue then you can just select those four, so you only need to enumerate the cases where each residue appears at most three times

[rapid vortex]

Consider the 7 numbers modulo 4, gives us 4 possible remainders: 0, 1, 2, and 3.

right

[shut obsidian]

Exactly

[cinder sequoia]

so it's just a case for each way to distribute the residues among seven numbers where no residue appears more than thrice

[cinder sequoia]

if 3 numbers have residue 0, then you know that there must be 4 other numbers that have either residue 1,2, or 3

[shut obsidian]

Yes

[cinder sequoia]

hm you're right there's still a lot of cases

[shut obsidian]

Just for the case where it's 3 on = 0

Now for 2, there will be even more?

[shut obsidian]

Wait, maybe it checks out

My teacher had like 10-15

Maybe we'll end up with an order around that too?

[cursive patrol]

40

[shut obsidian]

Oh

[cinder sequoia]

^^

i know it's gpt so not too trustworthy but this is kind of the reasoning for counting the cases

when you expand (1 + x + x^2 + x^3)^4 you find a 40x^7 term

[cursive patrol]

to end up 0 mod 4, you would need to pick residues: 3100 2200 2110 3320 3311 3221

and you can eliminate all cases with this fact

[shut obsidian]

Wdym

[cursive patrol]

the possible case structures are

[hearty spoke]

If you're not insistent on going through a lot of cases, it is easier to prove a lemma that for any set of 3 distinct natural numbers, you can select two of them so that the sum is divisible by 2. You can then apply this lemma to your problem to get subsets of your set of 7 numbers that are easier to work with.

[cursive patrol]

3-3-1-0
3-2-2-0
3-2-1-1
2-2-2-1

for picking the 7 numbers

[shut obsidian]

I might be misremembering but as if I recall my teacher had like 12-15 cases for this, I'm really not sure why we're getting this many

[cursive patrol]

and it is not strenuous to show that each of these patterns can be found no matter how any of the structures are arranged

[shut obsidian]

Ok my teacher had more than just those

This is really weird

Maybe I'm just misremembering and it was a smaller problem

[cursive patrol]

these are the 40 cases just unordered btw

[cursive patrol]

the idea is that each of these structures have 3 non-empty boxes and there's always a box with at least 2 entries in it

[cursive patrol]

relate that to the possible residues you can pick: each of these has a repeated digit of 0, 1, 2, 3... and either repeats another digit or has the 2 other different digits

therefore no matter which of the 40 cases you choose, you will find at least one of the valid 4 residues

(idk how the alleged 10-15 number could arise)

[shut obsidian]

Are these all the cases already, maybe?

[cursive patrol]

that's 10 out of 40

[shut obsidian]

Maybe these are "special" 10 out of 40?

Like exactly the 10 that could give us difficulties and the 30 others are "clear"?

[cursive patrol]

all 40 are clear in the same way using the method i outlined above

it's possible there's something special about these 10 but i don't think the distinction is obvious

these 10 contain all 4 cases from 2-2-2-1 and 6 of 12 cases from 1-1-2-3 (the 6 cases where the 2 is arranged before the 3)

what these have in common is that they're the structures that use up all 4 bins

[cursive patrol]

i think the proof you saw showed that 3 bins always works, which would explain why you didn't write down any cases involving 3-3-1-0 or 3-2-2-0

and to explain it only using 6 / 12 of the 1-1-2-3 cases, i believe it didn't disambiguate between the 2 and 3 because a 3-peated residue isn't featured in any of the residue groupings

all this is way too shaky

[shut obsidian]

hmm

In a similar proof, we used "at least"

But here, this can't be that

[shut obsidian]

This was a similar one:

For 5 numbers

And divisible by 3

"mind." = "atleast"

I think the last case is unnecessary

My teacher wasn't paying attention there or something

[shut obsidian]

Can we do this one with this "at least method" too?

Or is that not useful here

[hearty spoke]

What exactly are you trying to accomplish here? Are you trying to figure out exactly what your instructor was doing or are you trying to just solve the problem.

[shut obsidian]

Trying to solve the problem with a similar, case-based approach as my instructor

That seemed very quick, you just write out the cases and after 10 or so you are done

[hearty spoke]

Okay, I just don't understand your instructors motivation for doing it this way when you can just split it up into much fewer than that. It just seems like it is teetering on a proof by exhaustion.

[shut obsidian]

I think his motivation is to do it more brute-forcy, without having to come up with elegant ways to do this

Let me re-post all of this so it isn't flooded

.close

[topaz sinew]

Channel closed

Closed by @shut obsidian

Use .reopen if this was a mistake.

[shut obsidian]

Ok wait I think I know why we have much less cases

N starts at 1 in this course

So I can just brute-force it, right?

nvm

[hearty spoke]

I don't see how that is relevant, and this problem isn't really of interest to me because of the way you phrased it.

From my understanding, you have a lot of cases, and you want to abuse some cleverness and symmetry, but not too much so that it remains an arduous task of covering a large number of cases. That's just too vague a restriction and I don't think that yields anything pedagogically interesting.

Anyway good luck

[shut obsidian]

Alright, thanks

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hybrid mirage]

I know this needs the Alternating Series Test

but I get confused on how you prove the second condition

cause the limit of a sub n does go to 0

but how do you show that a sub n + 1 is less than or equal to a sub n?

[cinder sequoia]

i mean in general to show that something is decreasing, why not take its derivative?

[hybrid mirage]

of the whole series?

[cinder sequoia]

of the nonalternating part

n^2/sqrt(n^6 + 4)

you'll of course only be concerned about what the derivative looks like after n = 1

[hybrid mirage]

ok

[cinder sequoia]

though you could expect this thing to be decreasing after some point since you know that n^2/sqrt(n^6+4) asymptotically behaves like 1/n

[hybrid mirage]

could I also just plug in values for n for the non-alternating part?

so for n+1, when n=1, it'd be (2)^2/sqrt(2)^6+4

then do that for 4 terms of n

and see if it's always less than or when n is >= some n-value

[cinder sequoia]

i mean that's not really a "proof" of it

[hybrid mirage]

fr?

damn

well, then i'll use the way you said

additionally, how do you check if an alternating series is conditional or not

[topaz sinew]

@hybrid mirage Has your question been resolved?

[hybrid mirage]

@cinder sequoia

breh

.close

[topaz sinew]

Channel closed

Closed by @hybrid mirage

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[jaunty venture]

If I have a graph and I want to partition in into euler paths. How would I find the minimum number of partitions?

[jaunty venture]

I know how to show whether or not a graph is an Euler path.

[topaz sinew]

@jaunty venture Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[agile umbra]

Hello, I'm looking through SAT question and this one stump me. Can someone help this out?

[agile umbra]

also when reply please tag me 🙏

[topaz sinew]

@agile umbra Has your question been resolved?

[neon iron]

I can help

[agile umbra]

please do

[neon iron]

@agile umbra

Got it

[agile umbra]

Where do I start?

[neon iron]

At the start, you will notice there are 23 integers total on both

It also says equal or greater than

Lowest data set a is 910 sum and data set b is 910 sum as highest integer sum

They will have the same mean since there are 23 integers total with same sum so the mean would be 910 divided by 23

Does that answer your question?

[agile umbra]

oh oh I get it now, thank you very much, tho the question does say less than the last interval so I think the answer is should be [d] instead?

[neon iron]

The question is "What is the smallest possible difference between the mean of data set A and the mean of data set B?"

It's saying the smallest difference between the data sets A and B's mean

Would be zero

Answer d is 23 and answer a is 0 which has no difference

[agile umbra]

It shouldn't be the same tho, it says greater or equal to lower number but less than the higher number. Tho I might mistake something

But yeah, the answer if my assumption is correct it should be (910-887)/23=1

I have to check my understanding further

[neon iron]

Wait i think i might read the question wrong

[agile umbra]

We both do didnt we

[neon iron]

Yeah i think so

Wait im getting confused

[agile umbra]

Still I think beside the part I pointed out, you're correct

[neon iron]

Also what is interval

Idk what it is

[agile umbra]

I think It just represent the range between the 2 stated number (10-20, 20-30, so on)

Anyway, thanks so much, I got it from here

[neon iron]

👍

[agile umbra]

Have a great day

[neon iron]

Gl on SAT

U too

[agile umbra]

.solved

[topaz sinew]

Channel closed

Closed by @agile umbra

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[knotty glen]

let A, B, C be the roots of P(x) = 2x^3 - 5x^2 + 4x - 9. What is the value of 1/A + 1/B + 1/C

[knotty glen]

i forgot how

[restive inlet]

combine those terms into a single fraction

and the numerator and denominator can be optained from veitas

[knotty glen]

thanks @restive inlet

.close

[topaz sinew]

Channel closed

Closed by @knotty glen

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[winged depot]

Hello

[winged depot]

Can someone explain to me why the first root is followed by a + sign, and then after the derivative of the root is ×(2x+2)

[unreal kite]

the + comes from product rule, the $\times$ comes from the chain rule.

[thorny flame]

Crystopher

[topaz sinew]

@winged depot Has your question been resolved?

[winged depot]

Oh ok

.close

[topaz sinew]

Channel closed

Closed by @winged depot

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[hard bluff]

Determine the size of an outdoor pool with a square bottom with a volume of 32 m^3 so that the least amount of materials is used for lining its walls and bottom. Specify the surface area of the pool (bottom and walls) in the response

[topaz sinew]

@hard bluff Has your question been resolved?

[topaz sinew]

@hard bluff Has your question been resolved?

[keen raptor]

ok let's make h the height, l the length, and w the width

how can we write that the volume is 32 in terms of these

[topaz sinew]

@hard bluff Has your question been resolved?

Channel closed

Closed by @hard bluff

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[winged brook]

it says that the answer to 16 is D and to 17 is D , is it correct?

[dense crescent]

Nop

Normality is twice of molarity

[winged brook]

so there's a mistake in the book

I thought so too

the correct answer in 16 is b and the correct answer in 17 is d so its the opposite

this is what the book says

[topaz sinew]

@winged brook Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[empty galleon]

Hi. How do i continue

[modern rock]

well for starters

it should be positive sin x

also are u sure this is the entire question?

i feel like it should be 2cosx-sinx

oh wait

i have tumour

[neon iron]

square it

might help

the first one

[modern rock]

u can expand 1

into cos^2 x + sin^2 x

and then -2sinxcosx

combines to make (cosx-sinx)^2

[ivory sorrel]

can I suggest another method $sin(2x) \leq \sqrt{2} sin(\frac{\pi}{4}-x)$

[thorny flame]

ƒ(Why am. I here)=I don't Know

[ivory sorrel]

now square both sides and solve

[hollow plover]

Is that 1?

•_•

[modern rock]

yeah

i have seen a one drawn like that so many times

i dont get why

[hollow plover]

Second step wrong here though

[modern rock]

yeah i already said that

[hollow plover]

Sry i didnt see

[modern rock]

all good

[empty galleon]

Yes

[empty galleon]

Okay

[empty galleon]

I see it now

Thanks yall

.close

[topaz sinew]

Channel closed

Closed by @empty galleon

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[ivory sorrel]

hint:- start by changing the base

another hint $\forall x\in (0,1), log(x)<0$

[thorny flame]

ƒ(Why am. I here)=I don't Know

[modern rock]

a^log_a(x)=x

this would be handy here

[ivory sorrel]

I think changing the base may be better first, as the sign will change

[tawny elm]

Why is x between 0 and 1

[modern rock]

its not that x is between 0 and 1

[ivory sorrel]

when you apply the change of base rule, you'll have to compute log(1/3)

chose an appropriate base keeping that in mind

[tawny elm]

Is this wrong

[ivory sorrel]

what did you change the base to?

ah

looks alright to me

wait

one minute

[tawny elm]

Answer is 0,1 union 1,3

[ivory sorrel]

that would be 1/sqrt3, no?

the right hand side

[tawny elm]

No

Base power

Is -1

[ivory sorrel]

right

,w solve \sqrt{x^2-2x} < \sqrt{3}

[thorny flame]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by physicsrocks

[tawny elm]

Yea 2,3

[ivory sorrel]

so $\sqrt{x^2-2x} < \sqrt{3 \implies x^2-2x<3 }$

[thorny flame]

ƒ(Why am. I here)=I don't Know

[ivory sorrel]

or

[tawny elm]

I got 2,3

[ivory sorrel]

$\sqrt{x^2-2x} > -\sqrt{3}$

I think

[thorny flame]

ƒ(Why am. I here)=I don't Know

[tawny elm]

Idk where -1 and 0 comes from

[tawny elm]

Ohh

[ivory sorrel]

,w solve x^2-2x<3

[thorny flame]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by physicsrocks

[tawny elm]

So two cases

[ivory sorrel]

yeah, take their intersection

,w plot \sqrt{x^2-2x}<\sqrt{3}

[thorny flame]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by physicsrocks

[tawny elm]

Wait can you explain

From beginning

[ivory sorrel]

ok, can I do it my way? or should I do it your way

$\frac{log_3(\sqrt{x^2-2x}}{log_3(3^{-1}}) > -1/2$

[thorny flame]

ƒ(Why am. I here)=I don't Know

[ivory sorrel]

so you have

$log_3(\sqrt{x^2-2x})<\frac{1}{2}$

[thorny flame]

ƒ(Why am. I here)=I don't Know

[ivory sorrel]

so $0<\sqrt{x^2-2x}<\sqrt3$

[thorny flame]

ƒ(Why am. I here)=I don't Know

[ivory sorrel]

yes?

,w $0<\sqrt{x^2-2x}<\sqrt3$

[thorny flame]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by physicsrocks

[ivory sorrel]

now solve this

[tawny elm]

Ye

[ivory sorrel]

like here notice two things

one :- $x^2>2x$

[thorny flame]

ƒ(Why am. I here)=I don't Know

[ivory sorrel]

and two $x^2-2x<3$

[thorny flame]

ƒ(Why am. I here)=I don't Know

[tawny elm]

I did that

😭😭

[ivory sorrel]

where?

find the intersection of these two regions and you have your answer

sorry for misleading you earlier

[ivory sorrel]

.

[tawny elm]

Thabjs

Thanks

.close

[topaz sinew]

Channel closed

Closed by @tawny elm

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[clear wing]

If 1/a,1/b,1/c are in H.P , then 100^a , 100^b , 100^c will be in:
A) A.P
B) G.P
C) H.P
D) None of these

[topaz sinew]

@clear wing Has your question been resolved?

[eternal wing]

What have you tried?

[clear wing]

I try to make it A.P

i turn H.P into A.P

[eternal wing]

Yeah, so what is an A.P here?

[clear wing]

b-a and c-b

[eternal wing]

If 1/a, 1/b, 1/c are in an H.P then...?

[clear wing]

a,b,c in A.P

[eternal wing]

Why are you separating them?

Yes

a, b, c

Three consecutive elements in an arithmetic progression

Now what can you say about 100^a, 100^b, 100^c?

[clear wing]

no idea

can not understand it purpose

[eternal wing]

How can you express 100^b in terms of 100^a?

b is a + d, for some d

right?

[clear wing]

hmm

[eternal wing]

That means 100^b is 100^(a + d)

Which is what?

[clear wing]

100^(a+d)

[eternal wing]

Simplify it a little

[clear wing]

100^a +100^d

[eternal wing]

No

Recall the exponent rules

$a^{x + y} = a^x \cdot a^y$

[thorny flame]

RedstonePlayz09

[clear wing]

ohhhh right

sorry got it

[eternal wing]

Alright so what is 100^(a+d)?

[clear wing]

100^a * 100^d

base same power add

[eternal wing]

Ok, so 100^b is 100^a times 100^d

Do the same for b and c, since c = b + d

100^c will be 100^b times 100^d

Do you agree?

[clear wing]

yup

[eternal wing]

And 100^d is just some constant

Meaning to get from 100^a to 100^b, you multiply by that constant

and to get from 100^b to 100^c, you multiply by it again

And this means that...?

[clear wing]

G.P

right

[eternal wing]

Yes

[clear wing]

thank you

[eternal wing]

Np!

[keen raptor]

=p!

[eternal wing]

what

oh

is it tho

prove it

[clear wing]

bro one more thing

The ratio is not same

[eternal wing]

It is

[clear wing]

let me do it again

i do some mistake

[eternal wing]

$\frac{100^c}{100^b} = 100^{c-b}$

[thorny flame]

RedstonePlayz09

[clear wing]

when we are dividing 100^c/100^b

Where c = d+b why not taking b = d + c

[keen raptor]

what

because it isn't true

oh

I mean we could choose a different value of d that makes it true

but it makes more sense to go forward. c comes after b so it's b+d

b comes after a so it's a+d

[clear wing]

take ration of 100^c/100^b

and put values of c and b you can see ratio is not same

and do this with 100^b/100^a

[keen raptor]

the ratio is 100^d

[clear wing]

if u got same ratio let know

How

??

[keen raptor]

^

[clear wing]

bro their are three term 100^a , 100^b , 100^c

yes

if you say 100^c/100^b = 100^c-b

then 100^b/100^a = 100^b-a

[keen raptor]

What do you mean if you say

[clear wing]

ohh

[keen raptor]

That's how exponents work

[clear wing]

got it

100^c-b = 100^d and 100^b-a = 100^d

Thanks Man

For helping

i got my solution thanks again

.close

[topaz sinew]

Channel closed

Closed by @clear wing

Use .reopen if this was a mistake.

[keen raptor]

Np

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rotund maple]

Hi and I hope everybody is doing well

[rotund maple]

So We learnt in high school all about exp function & natural logarithms even logs with different bases

Ik how to solve basic equations involving exp and ik how to solve ofc quadratics

but here A friend proposed me a mix of both

i'll try to show it nicely

if it was something like this

I would substitute X = e^x

then solve with quadratic formula & at last solve for X1,X2=e^x ofc

but here isn't the case

we never learnt this is school

i feel like it isn't our level

[restive inlet]

would advise against using stuff that look like x when using substitution
exponentials don't mix well with stuff like (non-constant) polynomials,
no nice way to solve that

[rotund maple]

Yeah of course

But what would your approach be for that equation

I'm really curious

[restive inlet]

you can get decent approximations with stuff like
newtons method

[chilly walrus]

no exact solution exists to this, only approximations

[rotund maple]

i saw that lol

[rotund maple]

Never used it, but always eager to learn

[rotund maple]

May you show me a small example to get an approx of the solutions

[chilly walrus]

wolframalpha gives these as solutions

[rotund maple]

I already checked wolframalpha before i even joined discord

and symbolab as well

no steps sadly

[chilly walrus]

newton's method is the easiest type of approximation but it'll be quite annoying to do without a calculator

also bisection method exists

[rotund maple]

Interesting methods I see

[chilly walrus]

if you can sketch your target function that would make things easier but i assume you can't do that

[rotund maple]

i'm sorry i'm just a high schooler, but what do you exactly mean by the term "sketch"

[chilly walrus]

like make a rough plot

[rotund maple]

ah ok

[chilly walrus]

this is what it looks like

like a parabola but not quite

[chilly walrus]

actually since both solutions are less than zero here, e^(2x) is quite small so these are close to the solutions of x^2+4x=0, namely -4 and 0

[rotund maple]

yeah yeah

[rotund maple]

well noticed my friend

So, to conclude: exact(real) solutions don't exist for that equation but only approximations, approximate x values that would approach 0 when you replace them in the given polynomial

[rotund maple]

Oh yeah, cuz lim x-> -inf e^x = 0

means its getting smaller & smaller as it approaches negative, makes sense why the solutions given on wolframalpha are similar to x²+4x=0

[chilly walrus]

real means something different in math but yes there are no exact (closed-form) solutions to this

and approximations can be as exact as you wish but never completely exact

[rotund maple]

I mean i'm always solving for R anyways when it comes to those polynomials anyway lol

[chilly walrus]

so yeah

[rotund maple]

unless we are doing complex numbers

i mean we studied them as well, but meh

[rotund maple]

gotcha

[rotund maple]

X can't be exact like X= e-2 or X=sqrt(2) for example

which makes maths sexy in my opinion

cuz i needn't to calculate or to approx it

just simplify it and the teachers will shut up

Appreciate your help guys

.close

[topaz sinew]

Channel closed

Closed by @rotund maple

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[worldly solar]

can i write 5 - 3x^2 + 6x ≡ -3x^2 + 6x + 5

[worldly solar]

or

can i write 5 - 3x^2 + 6x <=> -3x^2 + 6x + 5

[chilly walrus]

just write = 🤔

context?

[worldly solar]

in general

[fiery dirge]

In this case both are true! I'd write = since it's just rewritten

[worldly solar]

ty

.solved

[topaz sinew]

Channel closed

Closed by @worldly solar

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dawn abyss]

log_6 x is the range all positive numbers?

[loud oasis]

it is not. remember that the range is all possible outputs of a function

[loud oasis]

none of those answer options correspond to this statement

[dawn abyss]

the answer choice is 1 not 4

how?

[loud oasis]

we are looking for a false statement. it's true that the range of the function is all real numbers

but it does not have an asymptote described by y = 0

[dawn abyss]

how is that true?

[loud oasis]

the function log_6 x can output every real number

[dawn abyss]

but when u graph it, it only goes to quad 1

[loud oasis]

it occupies quadrants 1 and 4

,w graph y = log_6(x)

[thorny flame]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by cloudedhorizons

[dawn abyss]

but thats so

small

[loud oasis]

it asymptotes all the way to -infinity between 0 and 1

[dawn abyss]

thats all real numbers?

[loud oasis]

that's all negative real numbers. then it outputs all positive real numbers between x = 1 and infinity

[dawn abyss]

alr thank you

.close

[topaz sinew]

Channel closed

Closed by @dawn abyss

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[dreamy radish]

i need some help with some representation theory stuff

[dreamy radish]

this is the question

i need some help understanding the solution

given the defining representation of Sn is an nxn matrix

with every column containing only 1 number 1 and rest zeros

how does this fit in

[topaz sinew]

@dreamy radish Has your question been resolved?

[topaz sinew]

@dreamy radish Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[neon iron]

can someone real q

link me to a d erivation of a similiar sum

.close

[topaz sinew]

Channel closed

Closed by @worthy cairn

Use .reopen if this was a mistake.

[half edge]

@neon iron what is this for

PV of what

[neon iron]

a stock

with a constant growth of g

[half edge]

as a geometric annuity?

honestly not familiar with D_t so

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[crimson finch]

why is it 7! and not 6!

[glossy drift]

So in the case of xxxyzyzyz, they're treating xxx as a single letter, and then you have the other six letters for a total of 7 "letters"

you can say something like xxx=a to make it easier

[crimson finch]

ahhhh

so for 2 three-letter strings you treat them as a single letter, but you have 3 spots left (and 3 individual letters), so in total 5 "letters"

okay that makes sense thanks

[glossy drift]

yep exactly

[crimson finch]

.close

[topaz sinew]

Channel closed

Closed by @crimson finch

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[tall quiver]

Hello, I’m solving a problem and I’m the last step (orange) I have to factor (x^2 + x + 1^2)

What methods of factoring are available to factor the polynomial? (I want a list of the options I could use, just so I can practice each one).

Thank you.

[modern rock]

completing the squarte

quadratic formula

[restive inlet]

that doesn't have real/rational roots, so there's no nice factorisation for it

if you really wanted to factor it using complex numbers,
go through completeing the square / factorisation identity for difference of two squares

but from the question, if you just wanted solutions, you can use quad formula

[tall quiver]

What does it mean when it doesn’t have real/rational roots? Can you dumb it down for me @restive inlet

[restive inlet]

real numbers can be found on the number line, the roots of this aren't there
rational roots can be expressed as a fraction of two integers (you could extend that to include purely imaginary values like 3i)

[tall quiver]

Okay that makes sense because in this chapter we are learning about imaginary numbers and complex numbers, but how did you know the roots weren’t real numbers ?

Are the roots in the form of (x + _)(x - _)?

@restive inlet

[restive inlet]

roots won't have x in them

(x-m)(-n) will be the factored form
in that form, m,n will be the roots
here they won't be nice values

[pearl fog]

$\frac{-1\pm\sqrt{-3}}{2}$

[thorny flame]

Skill_Issue

[restive inlet]

you can do a quick check from the discriminant

[pearl fog]

ew

[tall quiver]

Roots are the actual answers to x right? @restive inlet

Like if you factored out of a polynomial and got (x+5) (x-6) then the roots would be -5 and 6 right?

[remote kindle]

roots are values ​​that zero a polynomial

[tall quiver]

Ok

Makes sense

But how did he know the roots aren’t on the real number line?

Just based on the polynomial

(x^2 + x + 1^2) = 0

How did @restive inlet know that this polynomial didn’t have roots on the real number line? Did he solve it, or is there a way to tell

[restive inlet]

you can do a quick check from the discriminant

[tall quiver]

I see, the discrimination is the square root (b^2 - 4(a)(c)) in the quadratic formula right?

Ok so if you do the square root of 1^2 - 4(1)(1) you get 1-4 = -3

And since the square root of -3 is an imaginary number, you knew the roots wouldn’t be on the real number line based off the discriminant alone? @restive inlet

[restive inlet]

yes

[tall quiver]

I see, ok. My last question is,

If I’m factoring a polynomial and not sure which method to use, can I always resort to quadratic method? I was told by someone when solving polynomials that I should try to eyeball it to see if I know a faster way to solve it (such as completing a square) but if I can’t think of any, to use the quadratic method. Does that make sense ? @restive inlet

[remote kindle]

if the polynomial is of degree 2

[tall quiver]

Okay if a polynomial has a degree of 2 then I can always use the quadratic method right @remote kindle

[remote kindle]

yes

[tall quiver]

Ok got it. Thx

[topaz sinew]

@tall quiver Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[grand solar]

I'm confused on what shape this makes? would it be a hyperbolic paraboloid like this?

[grand solar]

but rotated 90 degrees on the xy plane?

[raven sparrow]

More or less, yes

[topaz sinew]

@grand solar Has your question been resolved?

[topaz sinew]

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[inner dove]

any short hints

[ionic oar]

what did trig sub get you

[noble laurel]

[inner dove]

wtf this nawal moneky